Metanalysis of flow state in condition of Stereotype Threat (stThreat)

Geiser C. Challco geiser@alumni.usp.br

Initial Variables and Loading Data

cond <- "stThreat"
to_remove <- c('S11')
sub.groups <- c("age","ed.level","intervention","age:intervention",
                "ed.level:intervention","age:ed.level:intervention")
dat <- read_excel("../data/data-without-outliers.xlsx", sheet = "fss-cond-descriptive")
dat <- dat[!dat$study %in% to_remove, ]

leg <- read_excel("../data/data-without-outliers.xlsx", sheet = "legend")
## New names:
## • `` -> `...10`
leg <- leg[!leg$study %in% to_remove, ]

idx.e <- which(dat$condition==cond)
idx.c <- which(dat$condition=="control")

data <- data.frame(
  study = dat$study[idx.c],
  n.e = dat$N[idx.e], mean.e = dat$M.emms[idx.e], sd.e = dat$SD.emms[idx.e],
  n.c = dat$N[idx.c], mean.c = dat$M.emms[idx.c], sd.c = dat$SD.emms[idx.c]
)
for (cgroups in strsplit(sub.groups,":")) {
  data[[paste0(cgroups, collapse = ":")]] <- sapply(data$study, FUN = function(x) {
    paste0(sapply(cgroups, FUN = function(namecol) leg[[namecol]][which(x == leg$study)]), collapse = ":")
  })
}
data[["lbl"]] <- sapply(data$study, FUN = function(x) leg$Note[which(x == leg$study)])

Perform meta-analyses

m.cont <- metacont(
  n.e = n.e, mean.e = mean.e, sd.e = sd.e, n.c = n.c, mean.c = mean.c, sd.c = sd.c,
  studlab = lbl, data = data, sm = "SMD", method.smd = "Hedges",
  fixed = F, random = T, method.tau = "REML", hakn = T, title = paste("Performance in",cond)
)
summary(m.cont)
## Review:     Performance in stThreat
## 
##                               SMD             95%-CI %W(random)
## S1                         0.4174 [-0.0990;  0.9338]       11.0
## S2                         0.1925 [-0.2204;  0.6053]       14.3
## S3                        -0.2607 [-0.7823;  0.2610]       10.9
## S4                         0.2676 [-0.2677;  0.8028]       10.5
## S5                         0.3398 [-0.1285;  0.8082]       12.4
## S6                         0.2142 [-0.2581;  0.6865]       12.3
## S7                         0.3025 [-0.1003;  0.7053]       14.7
## S10: Only use prompt msgs -0.4296 [-0.8583; -0.0010]       13.8
## 
## Number of studies combined: k = 8
## Number of observations: o = 600
## 
##                         SMD            95%-CI    t p-value
## Random effects model 0.1274 [-0.1287; 0.3835] 1.18  0.2778
## 
## Quantifying heterogeneity:
##  tau^2 = 0.0393 [0.0000; 0.3290]; tau = 0.1981 [0.0000; 0.5736]
##  I^2 = 40.8% [0.0%; 73.9%]; H = 1.30 [1.00; 1.96]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  11.83    7  0.1063
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.cont, digits=2, digits.sd = 2, test.overall = T, label.e = cond)

Subgroup analysis by “age”

m.sg4sub <- update.meta(m.cont, subgroup = age, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Performance in stThreat
## 
##                               SMD             95%-CI %W(random)        age
## S1                         0.4174 [-0.0990;  0.9338]       11.0 adolescent
## S2                         0.1925 [-0.2204;  0.6053]       14.3 adolescent
## S3                        -0.2607 [-0.7823;  0.2610]       10.9 adolescent
## S4                         0.2676 [-0.2677;  0.8028]       10.5      adult
## S5                         0.3398 [-0.1285;  0.8082]       12.4      adult
## S6                         0.2142 [-0.2581;  0.6865]       12.3      adult
## S7                         0.3025 [-0.1003;  0.7053]       14.7      adult
## S10: Only use prompt msgs -0.4296 [-0.8583; -0.0010]       13.8 adolescent
## 
## Number of studies combined: k = 8
## Number of observations: o = 600
## 
##                         SMD            95%-CI    t p-value
## Random effects model 0.1274 [-0.1287; 0.3835] 1.18  0.2778
## 
## Quantifying heterogeneity:
##  tau^2 = 0.0393 [0.0000; 0.3290]; tau = 0.1981 [0.0000; 0.5736]
##  I^2 = 40.8% [0.0%; 73.9%]; H = 1.30 [1.00; 1.96]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  11.83    7  0.1063
## 
## Results for subgroups (random effects model):
##                    k     SMD            95%-CI  tau^2    tau    Q   I^2
## age = adolescent   4 -0.0251 [-0.6469; 0.5968] 0.0953 0.3088 8.09 62.9%
## age = adult        4  0.2839 [ 0.1999; 0.3680]      0      0 0.15  0.0%
## 
## Test for subgroup differences (random effects model):
##                     Q d.f. p-value
## Between groups   2.46    1  0.1171
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = cond)

Subgroup analysis by “ed.level”

m.sg4sub <- update.meta(m.cont, subgroup = ed.level, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Performance in stThreat
## 
##                               SMD             95%-CI %W(random)         ed.level
## S1                         0.4174 [-0.0990;  0.9338]       11.0  upper-secundary
## S2                         0.1925 [-0.2204;  0.6053]       14.3  upper-secundary
## S3                        -0.2607 [-0.7823;  0.2610]       10.9  upper-secundary
## S4                         0.2676 [-0.2677;  0.8028]       10.5 higher-education
## S5                         0.3398 [-0.1285;  0.8082]       12.4 higher-education
## S6                         0.2142 [-0.2581;  0.6865]       12.3 higher-education
## S7                         0.3025 [-0.1003;  0.7053]       14.7          unknown
## S10: Only use prompt msgs -0.4296 [-0.8583; -0.0010]       13.8  upper-secundary
## 
## Number of studies combined: k = 8
## Number of observations: o = 600
## 
##                         SMD            95%-CI    t p-value
## Random effects model 0.1274 [-0.1287; 0.3835] 1.18  0.2778
## 
## Quantifying heterogeneity:
##  tau^2 = 0.0393 [0.0000; 0.3290]; tau = 0.1981 [0.0000; 0.5736]
##  I^2 = 40.8% [0.0%; 73.9%]; H = 1.30 [1.00; 1.96]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  11.83    7  0.1063
## 
## Results for subgroups (random effects model):
##                               k     SMD            95%-CI  tau^2    tau    Q   I^2
## ed.level = upper-secundary    4 -0.0251 [-0.6469; 0.5968] 0.0953 0.3088 8.09 62.9%
## ed.level = higher-education   3  0.2748 [ 0.1118; 0.4377]      0      0 0.14  0.0%
## ed.level = unknown            1  0.3025 [-0.1003; 0.7053]     --     -- 0.00    --
## 
## Test for subgroup differences (random effects model):
##                     Q d.f. p-value
## Between groups   2.30    2  0.3160
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = cond)

Subgroup analysis by “intervention”

m.sg4sub <- update.meta(m.cont, subgroup = intervention, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Performance in stThreat
## 
##                               SMD             95%-CI %W(random)
## S1                         0.4174 [-0.0990;  0.9338]       11.0
## S2                         0.1925 [-0.2204;  0.6053]       14.3
## S3                        -0.2607 [-0.7823;  0.2610]       10.9
## S4                         0.2676 [-0.2677;  0.8028]       10.5
## S5                         0.3398 [-0.1285;  0.8082]       12.4
## S6                         0.2142 [-0.2581;  0.6865]       12.3
## S7                         0.3025 [-0.1003;  0.7053]       14.7
## S10: Only use prompt msgs -0.4296 [-0.8583; -0.0010]       13.8
##                                                                   intervention
## S1                        Gender-stereotype color, ranking, badges, and avatar
## S2                        Gender-stereotype color, ranking, badges, and avatar
## S3                        Gender-stereotype color, ranking, badges, and avatar
## S4                        Gender-stereotype color, ranking, badges, and avatar
## S5                        Gender-stereotype color, ranking, badges, and avatar
## S6                        Gender-stereotype color, ranking, badges, and avatar
## S7                        Gender-stereotype color, ranking, badges, and avatar
## S10: Only use prompt msgs      Gender-stereotyped motivational message prompts
## 
## Number of studies combined: k = 8
## Number of observations: o = 600
## 
##                         SMD            95%-CI    t p-value
## Random effects model 0.1274 [-0.1287; 0.3835] 1.18  0.2778
## 
## Quantifying heterogeneity:
##  tau^2 = 0.0393 [0.0000; 0.3290]; tau = 0.1981 [0.0000; 0.5736]
##  I^2 = 40.8% [0.0%; 73.9%]; H = 1.30 [1.00; 1.96]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  11.83    7  0.1063
## 
## Results for subgroups (random effects model):
##                                                      k     SMD             95%-CI tau^2 tau    Q  I^2
## intervention = Gender-stereotype color, rankin ...   7  0.2202 [ 0.0337;  0.4067]     0   0 4.28 0.0%
## intervention = Gender-stereotyped motivational ...   1 -0.4296 [-0.8583; -0.0010]    --  -- 0.00   --
## 
## Test for subgroup differences (random effects model):
##                     Q d.f. p-value
## Between groups   7.87    1  0.0050
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = cond)

Subgroup analysis by “age:intervention”

m.sg4sub <- update.meta(m.cont, subgroup = `age:intervention`, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Performance in stThreat
## 
##                               SMD             95%-CI %W(random)
## S1                         0.4174 [-0.0990;  0.9338]       11.0
## S2                         0.1925 [-0.2204;  0.6053]       14.3
## S3                        -0.2607 [-0.7823;  0.2610]       10.9
## S4                         0.2676 [-0.2677;  0.8028]       10.5
## S5                         0.3398 [-0.1285;  0.8082]       12.4
## S6                         0.2142 [-0.2581;  0.6865]       12.3
## S7                         0.3025 [-0.1003;  0.7053]       14.7
## S10: Only use prompt msgs -0.4296 [-0.8583; -0.0010]       13.8
##                                                                          age:intervention
## S1                        adolescent:Gender-stereotype color, ranking, badges, and avatar
## S2                        adolescent:Gender-stereotype color, ranking, badges, and avatar
## S3                        adolescent:Gender-stereotype color, ranking, badges, and avatar
## S4                             adult:Gender-stereotype color, ranking, badges, and avatar
## S5                             adult:Gender-stereotype color, ranking, badges, and avatar
## S6                             adult:Gender-stereotype color, ranking, badges, and avatar
## S7                             adult:Gender-stereotype color, ranking, badges, and avatar
## S10: Only use prompt msgs      adolescent:Gender-stereotyped motivational message prompts
## 
## Number of studies combined: k = 8
## Number of observations: o = 600
## 
##                         SMD            95%-CI    t p-value
## Random effects model 0.1274 [-0.1287; 0.3835] 1.18  0.2778
## 
## Quantifying heterogeneity:
##  tau^2 = 0.0393 [0.0000; 0.3290]; tau = 0.1981 [0.0000; 0.5736]
##  I^2 = 40.8% [0.0%; 73.9%]; H = 1.30 [1.00; 1.96]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  11.83    7  0.1063
## 
## Results for subgroups (random effects model):
##                                                          k     SMD             95%-CI  tau^2    tau    Q
## age:intervention = adolescent:Gender-stereotype co ...   3  0.1247 [-0.6949;  0.9444] 0.0403 0.2008 3.43
## age:intervention = adult:Gender-stereotype color,  ...   4  0.2839 [ 0.1999;  0.3680]      0      0 0.15
## age:intervention = adolescent:Gender-stereotyped m ...   1 -0.4296 [-0.8583; -0.0010]     --     -- 0.00
##                                                          I^2
## age:intervention = adolescent:Gender-stereotype co ... 41.7%
## age:intervention = adult:Gender-stereotype color,  ...  0.0%
## age:intervention = adolescent:Gender-stereotyped m ...    --
## 
## Test for subgroup differences (random effects model):
##                      Q d.f. p-value
## Between groups   11.09    2  0.0039
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = cond)

Subgroup analysis by “ed.level:intervention”

m.sg4sub <- update.meta(m.cont, subgroup = `ed.level:intervention`, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Performance in stThreat
## 
##                               SMD             95%-CI %W(random)
## S1                         0.4174 [-0.0990;  0.9338]       11.0
## S2                         0.1925 [-0.2204;  0.6053]       14.3
## S3                        -0.2607 [-0.7823;  0.2610]       10.9
## S4                         0.2676 [-0.2677;  0.8028]       10.5
## S5                         0.3398 [-0.1285;  0.8082]       12.4
## S6                         0.2142 [-0.2581;  0.6865]       12.3
## S7                         0.3025 [-0.1003;  0.7053]       14.7
## S10: Only use prompt msgs -0.4296 [-0.8583; -0.0010]       13.8
##                                                                           ed.level:intervention
## S1                         upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S2                         upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S3                         upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S4                        higher-education:Gender-stereotype color, ranking, badges, and avatar
## S5                        higher-education:Gender-stereotype color, ranking, badges, and avatar
## S6                        higher-education:Gender-stereotype color, ranking, badges, and avatar
## S7                                 unknown:Gender-stereotype color, ranking, badges, and avatar
## S10: Only use prompt msgs       upper-secundary:Gender-stereotyped motivational message prompts
## 
## Number of studies combined: k = 8
## Number of observations: o = 600
## 
##                         SMD            95%-CI    t p-value
## Random effects model 0.1274 [-0.1287; 0.3835] 1.18  0.2778
## 
## Quantifying heterogeneity:
##  tau^2 = 0.0393 [0.0000; 0.3290]; tau = 0.1981 [0.0000; 0.5736]
##  I^2 = 40.8% [0.0%; 73.9%]; H = 1.30 [1.00; 1.96]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  11.83    7  0.1063
## 
## Results for subgroups (random effects model):
##                                                               k     SMD             95%-CI  tau^2    tau
## ed.level:intervention = upper-secundary:Gender-stereoty ...   3  0.1247 [-0.6949;  0.9444] 0.0403 0.2008
## ed.level:intervention = higher-education:Gender-stereot ...   3  0.2748 [ 0.1118;  0.4377]      0      0
## ed.level:intervention = unknown:Gender-stereotype color ...   1  0.3025 [-0.1003;  0.7053]     --     --
## ed.level:intervention = upper-secundary:Gender-stereoty ...   1 -0.4296 [-0.8583; -0.0010]     --     --
##                                                                Q   I^2
## ed.level:intervention = upper-secundary:Gender-stereoty ... 3.43 41.7%
## ed.level:intervention = higher-education:Gender-stereot ... 0.14  0.0%
## ed.level:intervention = unknown:Gender-stereotype color ... 0.00    --
## ed.level:intervention = upper-secundary:Gender-stereoty ... 0.00    --
## 
## Test for subgroup differences (random effects model):
##                      Q d.f. p-value
## Between groups   10.58    3  0.0142
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = cond)

Subgroup analysis by “age:ed.level:intervention”

m.sg4sub <- update.meta(m.cont, subgroup = `age:ed.level:intervention`, random = T, fixed = F)
summary(m.sg4sub)
## Review:     Performance in stThreat
## 
##                               SMD             95%-CI %W(random)
## S1                         0.4174 [-0.0990;  0.9338]       11.0
## S2                         0.1925 [-0.2204;  0.6053]       14.3
## S3                        -0.2607 [-0.7823;  0.2610]       10.9
## S4                         0.2676 [-0.2677;  0.8028]       10.5
## S5                         0.3398 [-0.1285;  0.8082]       12.4
## S6                         0.2142 [-0.2581;  0.6865]       12.3
## S7                         0.3025 [-0.1003;  0.7053]       14.7
## S10: Only use prompt msgs -0.4296 [-0.8583; -0.0010]       13.8
##                                                                                 age:ed.level:intervention
## S1                        adolescent:upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S2                        adolescent:upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S3                        adolescent:upper-secundary:Gender-stereotype color, ranking, badges, and avatar
## S4                            adult:higher-education:Gender-stereotype color, ranking, badges, and avatar
## S5                            adult:higher-education:Gender-stereotype color, ranking, badges, and avatar
## S6                            adult:higher-education:Gender-stereotype color, ranking, badges, and avatar
## S7                                     adult:unknown:Gender-stereotype color, ranking, badges, and avatar
## S10: Only use prompt msgs      adolescent:upper-secundary:Gender-stereotyped motivational message prompts
## 
## Number of studies combined: k = 8
## Number of observations: o = 600
## 
##                         SMD            95%-CI    t p-value
## Random effects model 0.1274 [-0.1287; 0.3835] 1.18  0.2778
## 
## Quantifying heterogeneity:
##  tau^2 = 0.0393 [0.0000; 0.3290]; tau = 0.1981 [0.0000; 0.5736]
##  I^2 = 40.8% [0.0%; 73.9%]; H = 1.30 [1.00; 1.96]
## 
## Test of heterogeneity:
##      Q d.f. p-value
##  11.83    7  0.1063
## 
## Results for subgroups (random effects model):
##                                                                   k     SMD             95%-CI  tau^2
## age:ed.level:intervention = adolescent:upper-secundary:Gend ...   3  0.1247 [-0.6949;  0.9444] 0.0403
## age:ed.level:intervention = adult:higher-education:Gender-s ...   3  0.2748 [ 0.1118;  0.4377]      0
## age:ed.level:intervention = adult:unknown:Gender-stereotype ...   1  0.3025 [-0.1003;  0.7053]     --
## age:ed.level:intervention = adolescent:upper-secundary:Gend ...   1 -0.4296 [-0.8583; -0.0010]     --
##                                                                    tau    Q   I^2
## age:ed.level:intervention = adolescent:upper-secundary:Gend ... 0.2008 3.43 41.7%
## age:ed.level:intervention = adult:higher-education:Gender-s ...      0 0.14  0.0%
## age:ed.level:intervention = adult:unknown:Gender-stereotype ...     -- 0.00    --
## age:ed.level:intervention = adolescent:upper-secundary:Gend ...     -- 0.00    --
## 
## Test for subgroup differences (random effects model):
##                      Q d.f. p-value
## Between groups   10.58    3  0.0142
## 
## Details on meta-analytical method:
## - Inverse variance method
## - Restricted maximum-likelihood estimator for tau^2
## - Q-profile method for confidence interval of tau^2 and tau
## - Hartung-Knapp adjustment for random effects model
## - Hedges' g (bias corrected standardised mean difference; using exact formulae)
forest(m.sg4sub, digits=2, digits.sd = 2, test.overall = T, label.e = cond)

Funnel Plot

m.cont <- update.meta(m.cont, studlab = data$study)
summary(eggers.test(x = m.cont))
## Eggers' test of the intercept 
## ============================= 
## 
##  intercept        95% CI     t    p
##      0.883 -8.52 - 10.28 0.184 0.86
## 
## Eggers' test does not indicate the presence of funnel plot asymmetry.
funnel(m.cont, xlab = "Hedges' g", studlab = T, legend=T, addtau2 = T)